Prediction of seismic loadings on wind turbine support structures by response spectrum method considering equivalent modal damping of support structures and reliability level

Abstract

In this study, a new damping correction factor is proposed to provide an accurate design response spectrum for megawatt (MW) class wind turbines. The predicted response spectra show good agreement with those by time history analysis (THA).An equivalent modal damping of wind turbine support structures is then proposed for response spectrum method (RSM) based on the modal decomposition method for non-classically damped structures. Seismic loadings on wind turbine towers and footings by RSM with the proposed damping correction factor and equivalent modal damping are also investigated and compared with those by THA. Finally, a quantile value between 0.5 and 0.85 in the damping correction factor is calibrated to ensure the same reliability level as evaluated by THA currently used for estimation of seismic loadings on support structures. K E Y W O R D Sdamping correction factor, equivalent modal damping, reliability level, response spectrum method, seismic loading, wind turbine support structure

Seismic soil-structure interaction analysis of wind turbine support structures using augmented complex mode superposition response spectrum method

“…In this model, RNA is simplified as a lumped mass at the hub height (𝑘 = 𝑛) and is connected to the tower by using a rigid beam. This simplification has been verified not to influence the prediction accuracy of seismic loadings acting on the tower and footing, excluding that the bending moment at the hub height is underestimated because of no consideration of the mass moment of inertia of RNA (Kitahara and Ishihara, 2020). This bending moment though enables to be obtained as an additional loading by the angular acceleration at the hub height, which is further investigated in Section 2.4.…”

“…To cope with this issue, Ishihara et al (2011) have proposed a new damping correction factor for wind turbine support structures, in which the uncertainty in the response spectra is considered by employing a quantile value. Moreover, Kitahara and Ishihara (2020) have recently extended it to be applicable to MW class large sized wind turbine support structures as well.…”

“…An efficient method to account for the effect of SSI is to represent the soilstructure system as a seismic SSI model with a set of springs and dashpots at the soil-foundation interface, substituting the soil-foundation system. This method has been widely employed for the seismic analysis of wind turbine support structures (Bazeos et al, 2002;Butt and Ishihara, 2012;Stamatopoulos, 2013;Kitahara and Ishihara, 2020). However, by introducing the dashpots, the seismic SSI model is a non-classically damped system and thus classical modal damping models, such as Rayleigh damping model, cannot accurately represent its modal damping properties.…”

“…Although the modal damping ratios of non-classically damped systems can be theoretically obtained by the complex eigenvalue analysis, they cannot be directly used for RSM, since complex eigenmodes do not generally coincide with real eigenmodes, which is used in conventional RSM. To overcome this obstacle, Kitahara and Ishihara (2020) have proposed a modal decomposition method to identify equivalent modal damping ratios for the real eigenmodes from the modal damping ratios obtained by the complex eigenvalue analysis, and estimated seismic loadings on wind turbine support structures by conventional RSM using the identified modal damping ratios.…”

“…On the other hand, Gao et al (2019) have recently proposed complex mode superposition RSM for the non-classically damped systems to estimate maximum relative displacements based on the complex eigenmodes. This method employs the modal damping ratios obtained by the complex eigenvalue analysis, and thus it does not require the additional procedure to estimate the equivalent modal damping ratios for the real eigenmodes in Kitahara and Ishihara (2020). In this study, seismic loadings, i.e., maximum shear forces and bending moments, will be newly derived by this method to estimate those on wind turbine support structures.…”